The perimeter of a rectangle can be determined as the sum of twice its width and twice its length, following the formula:
[tex]P=2w+2l[/tex]
If you know the perimeter and length of a rectangle, you can determine its width using the formula.
The first step is to write the formula for w:
-pass 2l to the left side of the equal sign by applying the opposite operation to both sides of it:
[tex]\begin{gathered} P-2l=2w+2l-2l \\ P-2l=2w \end{gathered}[/tex]
-divide both sides by 2
[tex]\begin{gathered} 2w=P-2l \\ \frac{2w}{2}=\frac{P-2l}{2} \\ w=\frac{P-2l}{2} \end{gathered}[/tex]
You know that the rectangular garden has a perimeter of P=370ft, and its length is l=98ft, replace both values on the formula obtained for w:
[tex]\begin{gathered} w=\frac{P-2l}{2} \\ w=\frac{370-2\cdot98}{2} \\ w=\frac{370-196}{2} \\ w=\frac{174}{2} \\ w=87 \end{gathered}[/tex]
The width of the rectangular garden is 87ft
